# rebalancing based on dollar duration and CFA Volume 3 page 341 Example 7

CFA Volume 3 page 341 Example 7 Can someone explain how shorting Bond #2 can increase Dollar Duration of the portfolio ?

you are right, but don´t worry the problem is that both in example6 and example7 they f* up and calculated dollar duration as average instead of sum, is in the errata, check cfa website

just did the numbers initial dd = 111,945 new dd = 82,579 + I “need” 29,365 go get back to initial duration + #2 dd = 3,064 + if I only increase #2, new #dd = 3,064 + 29,365 = 32,430 + if I must have 32,430 dd using a bond with a duration of 0.305, means mkt value = 32,430 / (0.305/100) = 10,632,683 (compared to my current holding of roughly 1 mio mkt value) calculations are correct, but the example itself does not make a lot of sense

Thanks hala So in fact we have to add to our position not short ?

in this case, yes

or you can also do it without spending additional cash, by sellig some of your shorter duration bonds and using that cash to buy longer duration bonds, ofcourse you would need to do it in the right proportions

So according to this example a portfolio’s dollar duration is the sum of the individual secutiries’ dollar durations BUT isn’t a portfolio’s duration the WEIGHTED AVERAGE of the individual securities’ durations. Can someone clarify ?

Yes, Duration = Wght Avg Dollar Duration = sum